Multiplexing, also known as the concept of multiple transitions, is the set of chains that is stacked on top of an transition like GTR.
The goal of Multiplexing is to help create a transition that uses as much of the board as possible. Compared to a simple transition, Multiplexing helps prevent height differences between the two halves of the board.
Simple Transition
Look at the wasted space.
Multiplexing
Less wasted space.
Unlike most other chaining concepts in Puyo Puyo, there are no main Multiplexing "forms". (Not even in Japan!) Instead, Multiplexing is made up of several smaller shapes and patterns that can be arranged in multiple ways.
The first type of pattern is called a Canopy (also called a cushion, or zabuton). It is a line of Puyo that is 3 long. (There is also an variant that is 2-long.) This form can be stacked vertically.
A single 3-long Canopy.
A single 2-long Canopy.
Multiple stacked Canopies.
The second type of pattern is called an L-shape. It is a group of three Puyos shaped like an small L. Like the Canopy form, they can be placed on top of each other (if you group them in sets of two.)
A single L-shapes.
Multiple L-shapes.
The last type of pattern are the Regular Forms. They are the common Stairs and Sandwich patterns most beginners learn. In Multiplexing, they are combined with the other two forms above.
Recall that Stairs is a form where the falling Puyos connect to each other on the side. One type of Stairs used for Multiplexing is 1-3 Stairs. However, a variant of 2-2 Stairs is can also be used in Multiplexing. This variant is used with L-shapes and even with 1-3 Stairs itself.
3-1 Stairs.
2-2 Stairs variant + L-shape.
3-1 Stairs and 2-2 Variant.
With Sandwiches, you can use the the four normal variants (1-1-2/2-1-2/1-0-3/3-0-1) in Multiplexing. However, it is possible to get creative and use nonstandard forms in Multiplexing as well. (Remember that Sandwich form vertically surrounds on group of Puyos with another group of Puyos.)
Standard Green 2-1-1 Sandwich.
Nonstandard Blue Sandwich.
Green Sandwich + Yellow Stairs.
L-shapes + Canopy.
L-shapes + Stairs.
Canopy + Stairs + L-shape.
The video below will show examples of Multiplexing in an actual game. In these examples, focus on yuta (まはーら), who is the red player on the left.
Timestamps:
多重と組み替えのやり方/解説 by konkon_1123: An article that introduces the concepts of Multiplexing. An (Google) machine translation of the post can be found here.
【初心者講座】第二回 中盤戦の形、覚えておきたい多重折り by HageREN_2424: An article that shows beginner friendly examples of Multiplexing. An (Google) machine translation of the post can be found here.
多重組み替え公式集 by よしけん: An article that shows more examples of Multiple Stacking. An (Google) machine translation of the post can be found here.